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Because mod(x) is not "smooth at x = 0.
Suppose f(x) = mod(x). Then f'(x), if it existed, would be the limit, as dx tends to 0, of [f(x+dx) - f(x)]/dx
= limit, as dx tends to o , of [mod(x+dx) - mod(x)]/dx
When x = 0, this simplifies to mod(dx)/dx
If dx > 0 then f'(x) = -1
and
if dx < 0 then f'(x) = +1
Consequently f'(0) does not exist and hence the derivative of mod(x) does not exist at x = 0.
Graphically, it is because at x = 0 the graph is not smooth but has an angle.
Because mod(x) is not "smooth at x = 0.
Suppose f(x) = mod(x). Then f'(x), if it existed, would be the limit, as dx tends to 0, of [f(x+dx) - f(x)]/dx
= limit, as dx tends to o , of [mod(x+dx) - mod(x)]/dx
When x = 0, this simplifies to mod(dx)/dx
If dx > 0 then f'(x) = -1
and
if dx < 0 then f'(x) = +1
Consequently f'(0) does not exist and hence the derivative of mod(x) does not exist at x = 0.
Graphically, it is because at x = 0 the graph is not smooth but has an angle.
Because mod(x) is not "smooth at x = 0.
Suppose f(x) = mod(x). Then f'(x), if it existed, would be the limit, as dx tends to 0, of [f(x+dx) - f(x)]/dx
= limit, as dx tends to o , of [mod(x+dx) - mod(x)]/dx
When x = 0, this simplifies to mod(dx)/dx
If dx > 0 then f'(x) = -1
and
if dx < 0 then f'(x) = +1
Consequently f'(0) does not exist and hence the derivative of mod(x) does not exist at x = 0.
Graphically, it is because at x = 0 the graph is not smooth but has an angle.
Because mod(x) is not "smooth at x = 0.
Suppose f(x) = mod(x). Then f'(x), if it existed, would be the limit, as dx tends to 0, of [f(x+dx) - f(x)]/dx
= limit, as dx tends to o , of [mod(x+dx) - mod(x)]/dx
When x = 0, this simplifies to mod(dx)/dx
If dx > 0 then f'(x) = -1
and
if dx < 0 then f'(x) = +1
Consequently f'(0) does not exist and hence the derivative of mod(x) does not exist at x = 0.
Graphically, it is because at x = 0 the graph is not smooth but has an angle.
Wiki User
β 10y ago
Wiki User
β 10y agoBecause mod(x) is not "smooth at x = 0.
Suppose f(x) = mod(x). Then f'(x), if it existed, would be the limit, as dx tends to 0, of [f(x+dx) - f(x)]/dx
= limit, as dx tends to o , of [mod(x+dx) - mod(x)]/dx
When x = 0, this simplifies to mod(dx)/dx
If dx > 0 then f'(x) = -1
and
if dx < 0 then f'(x) = +1
Consequently f'(0) does not exist and hence the derivative of mod(x) does not exist at x = 0.
Graphically, it is because at x = 0 the graph is not smooth but has an angle.
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What is the derivative of 2lnx?
The derivative of ln x is 1/x The derivative of 2ln x is 2(1/x) = 2/x
Derivative of cosx?
The derivative of cos(x) is negative sin(x). Also, the derivative of sin(x) is cos(x).
What is the derivative of sinΟx?
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What is the derivative of csc x?
The derivative of csc(x) is -cot(x)csc(x).
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The derivative of sec(x) is sec(x) tan(x).
What is the derivative of cotx?
The derivative of cot(x) is -csc2(x).
What is the second derivitive of sec x?
Write sec x as a function of sines and cosines (in this case, sec x = 1 / cos x). Then use the division formula to take the first derivative. Take the derivative of the first derivative to get the second derivative. Reminder: the derivative of sin x is cos x; the derivative of cos x is - sin x.
What does the derivative graph mean?
I am assuming the you are talking about the graph of the derivative. The graph of the derivative of F(x) is the graph such that, for any x, the value of x on the graph of the derivative of F(x) is the slope at point x in F(x).
